Morse Theory and Persisten Homology for Toplogical Analysis of 3D Images of Complex Materials

Olaf Delgado-Friedrichs; Vanessa Robins; Adrian Sheppard

doi:10.1109/ICIP.2014.7025987

Morse Theory and Persisten Homology for Toplogical Analysis of 3D Images of Complex Materials

Olaf Delgado-Friedrichs, Vanessa Robins, Adrian Sheppard

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We develop topologically accurate and compatible definitions for the skeleton and watershed segmentation of a 3D digital object that are computed by a single algorithm. These definitions are based on a discrete gradient vector field derived from a signed distance transform. This gradient vector field is amenable to topological analysis and simplification via For-man's discrete Morse theory and provides a filtration that can be used as input to persistent homology algorithms. Efficient implementations allow us to process large-scale x-ray micro-CT data of rock cores and other materials.

Original language	English
Title of host publication	Proceedings of the 2014 IEEE International Conference on Image Processing (ICIP)
Place of Publication	USA
Publisher	IEEE Signal Processing Society
Pages	4872-4876
Edition	Peer Reviewed
ISBN (Print)	9781479957514
DOIs	https://doi.org/10.1109/ICIP.2014.7025987
Publication status	Published - 2014
Event	IEEE International Conference on Image Processing ICIP 2014 - Paris, France, France Duration: 1 Jan 2014 → …

Conference

Conference	IEEE International Conference on Image Processing ICIP 2014
Country/Territory	France
Period	1/01/14 → …
Other	October 27-30 2014

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10.1109/ICIP.2014.7025987

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title = "Morse Theory and Persisten Homology for Toplogical Analysis of 3D Images of Complex Materials",

abstract = "We develop topologically accurate and compatible definitions for the skeleton and watershed segmentation of a 3D digital object that are computed by a single algorithm. These definitions are based on a discrete gradient vector field derived from a signed distance transform. This gradient vector field is amenable to topological analysis and simplification via For-man's discrete Morse theory and provides a filtration that can be used as input to persistent homology algorithms. Efficient implementations allow us to process large-scale x-ray micro-CT data of rock cores and other materials.",

author = "Olaf Delgado-Friedrichs and Vanessa Robins and Adrian Sheppard",

year = "2014",

doi = "10.1109/ICIP.2014.7025987",

language = "English",

isbn = "9781479957514",

pages = "4872--4876",

booktitle = "Proceedings of the 2014 IEEE International Conference on Image Processing (ICIP)",

publisher = "IEEE Signal Processing Society",

edition = "Peer Reviewed",

note = "IEEE International Conference on Image Processing ICIP 2014 ; Conference date: 01-01-2014",

}

Delgado-Friedrichs, O , Robins, V & Sheppard, A 2014, Morse Theory and Persisten Homology for Toplogical Analysis of 3D Images of Complex Materials. in Proceedings of the 2014 IEEE International Conference on Image Processing (ICIP). Peer Reviewed edn, IEEE Signal Processing Society, USA, pp. 4872-4876, IEEE International Conference on Image Processing ICIP 2014, France, 1/01/14. https://doi.org/10.1109/ICIP.2014.7025987

Morse Theory and Persisten Homology for Toplogical Analysis of 3D Images of Complex Materials. / Delgado-Friedrichs, Olaf ; Robins, Vanessa ; Sheppard, Adrian.
Proceedings of the 2014 IEEE International Conference on Image Processing (ICIP). Peer Reviewed. ed. USA: IEEE Signal Processing Society, 2014. p. 4872-4876.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Morse Theory and Persisten Homology for Toplogical Analysis of 3D Images of Complex Materials

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AU - Robins, Vanessa

AU - Sheppard, Adrian

PY - 2014

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N2 - We develop topologically accurate and compatible definitions for the skeleton and watershed segmentation of a 3D digital object that are computed by a single algorithm. These definitions are based on a discrete gradient vector field derived from a signed distance transform. This gradient vector field is amenable to topological analysis and simplification via For-man's discrete Morse theory and provides a filtration that can be used as input to persistent homology algorithms. Efficient implementations allow us to process large-scale x-ray micro-CT data of rock cores and other materials.

AB - We develop topologically accurate and compatible definitions for the skeleton and watershed segmentation of a 3D digital object that are computed by a single algorithm. These definitions are based on a discrete gradient vector field derived from a signed distance transform. This gradient vector field is amenable to topological analysis and simplification via For-man's discrete Morse theory and provides a filtration that can be used as input to persistent homology algorithms. Efficient implementations allow us to process large-scale x-ray micro-CT data of rock cores and other materials.

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DO - 10.1109/ICIP.2014.7025987

M3 - Conference contribution

SN - 9781479957514

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EP - 4876

BT - Proceedings of the 2014 IEEE International Conference on Image Processing (ICIP)

PB - IEEE Signal Processing Society

CY - USA

T2 - IEEE International Conference on Image Processing ICIP 2014

Y2 - 1 January 2014

ER -

Morse Theory and Persisten Homology for Toplogical Analysis of 3D Images of Complex Materials

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